Energy principles and variational methods in applied mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2017
|
| Ausgabe: | Third edition |
| Schlagworte: | |
| Online-Zugang: | http://www.wiley-vch.de/publish/dt/books/ISBN978-1-119-08737-3/ Inhaltsverzeichnis |
| Beschreibung: | xxvi, 730 Seiten Illustrationen, Diagramme 24.4 cm x 17 cm, 1140 g |
| ISBN: | 9781119087373 1119087376 |
Internformat
MARC
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| 245 | 1 | 0 | |a Energy principles and variational methods in applied mechanics |c J. N. Reddy |
| 250 | |a Third edition | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2017 | |
| 300 | |a xxvi, 730 Seiten |b Illustrationen, Diagramme |c 24.4 cm x 17 cm, 1140 g | ||
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| 653 | |a Baustatik | ||
| 653 | |a Baustatik u. Baumechanik | ||
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| 653 | |a Computational / Numerical Methods | ||
| 653 | |a Festkörpermechanik | ||
| 653 | |a Maschinenbau | ||
| 653 | |a Mechanical Engineering | ||
| 653 | |a Mechanik | ||
| 653 | |a Rechnergestützte / Numerische Verfahren im Maschinenbau | ||
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Datensatz im Suchindex
| _version_ | 1804177961931243520 |
|---|---|
| adam_text | Contents
About the Author xvii
About the Companion Website xix
Preface to the Third Edition xxi
Preface to the Second Edition xxiii
Preface to the First Edition xxv
1 Introduction and Mathematical Preliminaries 1
1 1 Introduction 1
111 Preliminary Comments 1
112 The Role of Energy Methods and Variational Principles 1
113A Brief Review of Historical Developments 2
114 Preview 4
1 2 Vectors 5
121 Introduction 5
122 Definition of a Vector 6
123 Scalar and Vector Products 8
124 Components of a Vector 12
125 Summation Convention 13
126 Vector Calculus 17
127 Gradient, Divergence, and Curl Theorems 22
1 3 Tensors 26
131 Second-Order Tensors 26
132 General Properties of a Dyadic 29
133 Nonion Form and Matrix Representation of a Dyad 30
134 Eigenvectors Associated with Dyads 34
1 4 Summary 39
Problems 40
2 Review of Equations of Solid Mechanics 47
2 1 Introduction 47
211 Classification of Equations 47
212 Descriptions of Motion 48
2 2 Balance of Linear and Angular Momenta 50
221 Equations of Motion 50
222 Symmetry of Stress Tensors 54
CONTENTS
viii
2 3 Kinematics of Deformation 56
231 Green-Lagrange Strain Tensor 56
232 Strain Compatibility Equations 62
2 4 Constitutive Equations 65
241 Introduction 65
242 Generalized Hooke’s Law 66
243 Plane Stress-Reduced Constitutive Relations 68
244 Thermoelastic Constitutive Relations 70
2 5 Theories of Straight Beams 71
251 Introduction 71
252 The Bernoulli-Euler Beam Theory 73
253 The Timoshenko Beam Theory 76
254 The von Karman Theory of Beams 81
2541 Preliminary Discussion 81
2542 The Bernoulli-Euler Beam Theory 82
2543 The Timoshenko Beam Theory 84
2 6 Summary 85
Problems 88
3 Work, Energy, and Variational Calculus 97
3 1 Concepts of Work and Energy 97
311 Preliminary Comments 97
312 External and Internal Work Done 98
3 2 Strain Energy and Complementary Strain Energy 102
321 General Development 102
322 Expressions for Strain Energy and Complementary
Strain Energy Densities of Isotropic Linear Elastic Solids 107
3221 Stain energy density 107
3222 Complementary stain energy density 108
323 Strain Energy and Complementary Strain Energy
for Trusses 109
324 Strain Energy and Complementary Strain Energy
for Torsional Members 114
325 Strain Energy and Complementary Strain Energy
for Beams 117
3251 The Bernoulli-Euler Beam Theory 117
3252 The Timoshenko Beam Theory 119
CONTENTS
IX
3 3 Total Potential Energy and Total Complementary Energy 123
331 Introduction 123
332 Total Potential Energy of Beams 124
333 Total Complementary Energy of Beams 125
3 4 Virtual Work 126
341 Virtual Displacements 126
342 Virtual Forces 131
3 5 Calculus of Variations 135
351 The Variational Operator 135
352 Functionals 138
353 The First Variation of a Functional 139
354 Fundamental Lemma of Variational Calculus 140
355 Extremum of a Functional 141
356 The Euler Equations 143
357 Natural and Essential Boundary Conditions 146
358 Minimization of Functionals with Equality Constraints 151
3581 The Lagrange Multiplier Method 151
3582 The Penalty Function Method 153
3 6 Summary 156
Problems 159
4 Virtual Work and Energy Principles of Mechanics 167
4 1 Introduction 167
4 2 The Principle of Virtual Displacements 167
421 Rigid Bodies 167
422 Deformable Solids 168
423 Unit Dummy-Displacement Method 172
4 3 The Principle of Minimum Total Potential Energy and
Castigliano’s Theorem I 179
431 The Principle of Minimum Total Potential Energy 179
432 Castigliano’s Theorem I 188
4 4 The Principle of Virtual Forces 196
441 Deformable Solids 196
442 Unit Dummy-Load Method 198
4 5 Principle of Minimum Total Complementary Potential
Energy and Castigliano’s Theorem II 204
451 The Principle of the Minimum total Complementary
Potential Energy 204
452 Castigliano’s Theorem II 206
CONTENTS
4 6 Clapeyron’s, Betti’s, and Maxwell’s Theorems 217
461 Principle of Superposition for Linear Problems 217
462 Clapeyron’s Theorem 220
463 Types of Elasticity Problems and Uniqueness of Solutions 224
464 Betti’s Reciprocity Theorem 226
465 Maxwell’s Reciprocity Theorem 230
4 7 Summary 232
Problems 235
5 Dynamical Systems: Hamilton’s Principle 243
5 1 Introduction 243
5 2 Hamilton’s Principle for Discrete Systems 243
5 3 Hamilton’s Principle for a Continuum 249
5 4 Hamilton’s Principle for Constrained Systems 255
5 5 Rayleigh’s Method 260
5 6 Summary 262
Problems 263
6 Direct Variational Methods 269
6 1 Introduction 269
6 2 Concepts from Functional Analysis 270
621 General Introduction 270
622 Linear Vector Spaces 271
623 Normed and Inner Product Spaces 276
6231 Norm 276
6232 Inner product 279
6233 Orthogonality 280
624 Transformations, and Linear and Bilinear Forms 281
625 Minimum of a Quadratic Functional 282
6 3 The Ritz Method 287
631 Introduction 287
632 Description of the Method 288
633 Properties of Approximation Functions 293
6331 Preliminary Comments 293
6332 Boundary Conditions 293
6333 Convergence 294
6334 Completeness 294
6335 Requirements on 4 o and fa 295
634 General Features of the Ritz Method 299
CONTENTS Xi
635 Examples 300
636 The Ritz Method for General Boundary-Value Problems 323
6361 Preliminary Comments 323
6362 Weak Forms 323
6363 Model Equation 1 324
6364 Model Equation 2 328
6365 Model Equation 3 330
6366 Ritz Approximations 332
6 4 Weighted-Residual Methods 337
641 Introduction 337
642 The General Method of Weighted Residuals 339
643 The Galerkin Method 344
644 The Least-Squares Method 349
645 The Collocation Method 356
646 The Subdomain Method 359
647 Eigenvalue and Time-Dependent Problems 361
6471 Eigenvalue Problems 361
6472 Time-Dependent Problems 362
6 5 Summary 381
Problems 383
7 Theory and Analysis of Plates 391
7 1 Introduction 391
711 General Comments 391
712 An Overview of Plate Theories 393
7121 The Classical Plate Theory 394
7122 The First-Order Plate Theory 395
7123 The Third-Order Plate Theory 396
7124 Stress-Based Theories 397
7 2 The Classical Plate Theory 398
721 Governing Equations of Circular Plates 398
722 Analysis of Circular Plates 405
7221 Analytical Solutions For Bending 405
7222 Analytical Solutions For Buckling 411
7223 Variational Solutions 414
723 Governing Equations in Rectangular Coordinates 427
724 Navier Solutions of Rectangular Plates 435
7241 Bending 438
7242 Natural Vibration 443
7243 Buckling Analysis 445
7244 Transient Analysis 447
CONTENTS
xii
725 Levy Solutions of Rectangular Plates 449
726 Variational Solutions: Bending 454
727 Variational Solutions: Natural Vibration 470
728 Variational Solutions: Buckling 475
7281 Rectangular Plates Simply Supported along Two
Opposite Sides and Compressed in the Direction
Perpendicular to Those Sides 475
7282 Formulation for Rectangular Plates with
Arbitrary Boundary Conditions 478
7 3 The First-Order Shear Deformation Plate Theory 486
731 Equations of Circular Plates 486
732 Exact Solutions of Axisymmetric Circular Plates 488
733 Equations of Plates in Rectangular Coordinates 492
734 Exact Solutions of Rectangular Plates 496
7341 Bending Analysis 498
7342 Natural Vibration 501
7343 Buckling Analysis 502
735 Variational Solutions of Circular and Rectangular Plates 503
7351 Axisymmetric Circular Plates 503
7352 Rectangular Plates 505
7 4 Relationships Between Bending Solutions of Classical and
Shear Deformation Theories 507
741 Beams 507
7411 Governing Equations 508
7412 Relationships Between BET and TBT 508
742 Circular Plates 512
743 Rectangular Plates 516
7 5 Summary 521
Problems 521
8 The Finite Element Method 527
8 1 Introduction 527
8 2 Finite Element Analysis of Straight Bars 529
821 Governing Equation 529
822 Representation of the Domain by Finite Elements 530
823 Weak Form over an Element 531
824 Approximation over an Element 532
825 Finite Element Equations 537
8251 Linear Element 538
8252 Quadratic Element 539
CONTENTS XÜi
826 Assembly (Connectivity) of Elements 539
827 Imposition of Boundary Conditions 542
828 Postprocessing 543
8 3 Finite Element Analysis of the Bernoulli-Euler
Beam Theory 549
831 Governing Equation 549
832 Weak Form over an Element 549
833 Derivation of the Approximation Functions 550
834 Finite Element Model 552
835 Assembly of Element Equations 553
836 Imposition of Boundary Conditions 555
8 4 Finite Element Analysis of the Timoshenko Beam Theory 558
841 Governing Equations 558
842 Weak Forms 558
843 Finite Element Models 559
844 Reduced Integration Element (RIE) 559
845 Consistent Interpolation Element (CIE) 561
846 Superconvergent Element (SCE) 562
8 5 Finite Element Analysis of the Classical Plate Theory 565
851 Introduction 565
852 General Formulation 566
853 Conforming and Nonconforming Plate Elements 568
854 Fully Discretized Finite Element Models 569
8541 Static Bending 569
8542 Buckling 569
8543 Natural Vibration 570
8544 Transient Response 570
8 6 Finite Element Analysis of the First-Order Shear Deformation
Plate Theory 574
861 Governing Equations and Weak Forms 574
862 Finite Element Approximations 576
863 Finite Element Model 577
864 Numerical Integration 579
865 Numerical Examples 582
8651 Isotropic Plates 582
8652 Laminated Plates 584
8 7 Summary 587
Problems 588
XIV
CONTENTS
9 Mixed Variational and Finite Element Formulations 595
9 1 Introduction 595
911 General Comments 595
912 Mixed Variational Principles 595
913 Extremum and Stationary Behavior of Functionals 597
9 2 Stationary Variational Principles 599
921 Minimum Total Potential Energy 599
922 The Hellinger-Reissner Variational Principle 601
923 The Reissner Variational Principle 605
9 3 Variational Solutions Based on Mixed Formulations 606
9 4 Mixed Finite Element Models of Beams 610
941 The Bernoulli-Euler Beam Theory 610
9411 Governing Equations And Weak Forms 610
9412 Weak-Form Mixed Finite Element Model 610
9413 Weighted-Residual Finite Element Models 613
942 The Timoshenko Beam Theory 615
9421 Governing Equations 615
9422 General Finite Element Model 615
9423 ASD-LLCC Element 617
9424 ASD-QLCC Element 617
9425 ASD-HQLC Element 618
9 5 Mixed Finite Element Analysis of the Classical Plate Theory 620
951 Preliminary Comments 620
952 Mixed Model I 620
9521 Governing Equations 620
9522 Weak Forms 621
9523 Finite Element Model 622
953 Mixed Model II 625
9531 Governing Equations 625
9532 Weak Forms 625
9533 Finite Element Model 626
9 6 Summary 630
Problems 631
10 Analysis of Functionally Graded Beams and Plates 635
10 1 Introduction 635
10 2 Functionally Graded Beams 638
10 2 1 The Bernoulli-Euler Beam Theory 638
10 211 Displacement and strain fields 638
10 212 Equations of motion and boundary conditions 638
CONTENTS
XV
10 2 2 The Timoshenko Beam Theory 639
10 221 Displacement and strain fields 639
10 222 Equations of motion and boundary conditions 640
10 2 3 Equations of Motion in terms of Generalized
Displacements 641
10 231 Constitutive Equations 641
10 232 Stress Resultants of BET 641
10 233 Stress Resultants of TBT 642
10 234 Equations of Motion of the BET 642
10 235 Equations of Motion of the TBT 642
10 2 4 Stiffness Coefficients 643
10 3 Functionally Graded Circular Plates 645
10 3 1 Introduction 645
10 3 2 Classical Plate Theory 646
10 321 Displacement and Strain Fields 646
10 322 Equations of Motion 646
10 3 3 First-Order Shear Deformation Theory 647
10 331 Displacement and Strain Fields 647
10 332 Equations of Motion 648
10 3 4 Plate Constitutive Relations 649
10 341 Classical Plate Theory 649
10 342 First-Order Plate Theory 649
10 4 A General Third-Order Plate Theory 650
10 4 1 Introduction 650
10 4 2 Displacements and Strains 651
10 4 3 Equations of Motion 653
10 4 4 Constitutive Relations 657
10 4 5 Specialization to Other Theories 658
10 451A General Third-Order Plate Theory with
Traction-Free Top and Bottom Surfaces 658
10 452 The Reddy Third-Order Plate Theory 661
10 453 The First-Order Plate Theory 663
10 454 The Classical Plate Theory 664
10 5 Navier’s Solutions 664
10 5 1 Preliminary Comments 664
10 5 2 Analysis of Beams 665
10 521 Bernoulli-Euler Beams 665
10 522 Timoshenko Beams 667
10 523 Numerical Results 669
xvi
CONTENTS
10 5 3 Analysis of Plates 671
10 531 Boundary Conditions 672
10 532 Expansions of Generalized Displacements 672
10 533 Bending Analysis 673
10 534 Free Vibration Analysis 676
10 535 Buckling Analysis 677
10 536 Numerical Results 679
10 6 Finite Element Models 681
10 6 1 Bending of Beams 681
10 611 Bernoulli-Euler Beam Theory 681
10 612 Timoshenko Beam Theory 683
10 6 2 Axisymmetric Bending of Circular Plates 684
10 621 Classical Plate Theory 681
10 622 First-Order Shear Deformation Plate Theory 686
10 6 3 Solution of Nonlinear Equations 688
10 631 Times approximation 688
10 632 Newton’s Iteration Approach 688
10 633 Tangent Stiffness Coefficients for the BET 690
10 634 Tangent Stiffness Coefficients for the TBT 692
10 635 Tangent Stiffness Coefficients for the CPT 693
10 636 Tangent Stiffness Coefficients for the FSDT 693
10 6 4 Numerical Results for Beams and Circular Plates 694
10 641 Beams 694
10 642 Circular Plates 697
10 7 Summary 699
Problems 700
References 701
Answers to Most Problems 711
|
| any_adam_object | 1 |
| author | Reddy, Junuthula Narasimha 1945- |
| author_GND | (DE-588)108393232 |
| author_facet | Reddy, Junuthula Narasimha 1945- |
| author_role | aut |
| author_sort | Reddy, Junuthula Narasimha 1945- |
| author_variant | j n r jn jnr |
| building | Verbundindex |
| bvnumber | BV044577263 |
| classification_rvk | UF 1500 |
| ctrlnum | (OCoLC)1003588298 (DE-599)DNB1138579629 |
| dewey-full | 620 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620 |
| dewey-search | 620 |
| dewey-sort | 3620 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Physik |
| edition | Third edition |
| format | Book |
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| id | DE-604.BV044577263 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:56:24Z |
| institution | BVB |
| institution_GND | (DE-588)4101395-5 |
| isbn | 9781119087373 1119087376 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029975744 |
| oclc_num | 1003588298 |
| open_access_boolean | |
| owner | DE-M347 DE-Aug4 DE-83 |
| owner_facet | DE-M347 DE-Aug4 DE-83 |
| physical | xxvi, 730 Seiten Illustrationen, Diagramme 24.4 cm x 17 cm, 1140 g |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Wiley |
| record_format | marc |
| spelling | Reddy, Junuthula Narasimha 1945- (DE-588)108393232 aut Energy principles and variational methods in applied mechanics J. N. Reddy Third edition Hoboken, NJ Wiley 2017 xxvi, 730 Seiten Illustrationen, Diagramme 24.4 cm x 17 cm, 1140 g txt rdacontent n rdamedia nc rdacarrier Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Technische Mechanik (DE-588)4059231-5 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Bauingenieur- u. Bauwesen Baustatik Baustatik u. Baumechanik Civil Engineering & Construction Computational / Numerical Methods Festkörpermechanik Maschinenbau Mechanical Engineering Mechanik Rechnergestützte / Numerische Verfahren im Maschinenbau Solid Mechanics Structural Theory & Structural Mechanics Technische Mechanik (DE-588)4059231-5 s Mathematische Methode (DE-588)4155620-3 s Finite-Elemente-Methode (DE-588)4017233-8 s Variationsrechnung (DE-588)4062355-5 s DE-604 John Wiley and Sons (DE-588)4101395-5 pbl X:MVB http://www.wiley-vch.de/publish/dt/books/ISBN978-1-119-08737-3/ HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029975744&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reddy, Junuthula Narasimha 1945- Energy principles and variational methods in applied mechanics Variationsrechnung (DE-588)4062355-5 gnd Technische Mechanik (DE-588)4059231-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4059231-5 (DE-588)4017233-8 (DE-588)4155620-3 |
| title | Energy principles and variational methods in applied mechanics |
| title_auth | Energy principles and variational methods in applied mechanics |
| title_exact_search | Energy principles and variational methods in applied mechanics |
| title_full | Energy principles and variational methods in applied mechanics J. N. Reddy |
| title_fullStr | Energy principles and variational methods in applied mechanics J. N. Reddy |
| title_full_unstemmed | Energy principles and variational methods in applied mechanics J. N. Reddy |
| title_short | Energy principles and variational methods in applied mechanics |
| title_sort | energy principles and variational methods in applied mechanics |
| topic | Variationsrechnung (DE-588)4062355-5 gnd Technische Mechanik (DE-588)4059231-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Variationsrechnung Technische Mechanik Finite-Elemente-Methode Mathematische Methode |
| url | http://www.wiley-vch.de/publish/dt/books/ISBN978-1-119-08737-3/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029975744&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT reddyjunuthulanarasimha energyprinciplesandvariationalmethodsinappliedmechanics AT johnwileyandsons energyprinciplesandvariationalmethodsinappliedmechanics |